JEE Main 2026 · MathsMultiple choiceSingle correctHardMulti-step

JEE Main 2 April 2026, Shift 1, Maths Q14

Question 14 of 75 in this shift, Maths question 14 of 25, Section A.

\vec a

and

\vec b

are two vectors such that

|\vec a|=2

and

|\vec b|=3

, then the maximum value of

3\left|3\vec a+2\vec b\right|+4\left|3\vec a-2\vec b\right|

is :

(1) $30$
(2) $36$
(3) $60$ Official answer
(4) $72$

Official answer

Option 3

NTA final key.

Chapter: Vector Algebra
Topic: Dot Product
Idea tested: Parallelogram Law Identity

Same topic in other shifts

All Dot Product questions

2 Apr 2026, Shift 2 · Q14Let the vectors $\vec{a} = -\hat{i} + \hat{j} + 3\hat{k}$ and $\vec{b} = \hat{i} + 3\hat{j} + \hat{k}$ . For some…MediumSingle correct
2 Apr 2026, Shift 2 · Q16Two adjacent sides of a parallelogram $PQRS$ are given by $\vec{PQ} = \hat{j} + \hat{k}$ and $\vec{PS} = \hat{i} - \hat{j}$ . If the side…MediumSingle correct
2 Apr 2025, Shift 1 · Q11If $\vec{a}$ is a nonzero vector such that its projections on the vectors $2\hat{i}-\hat{j}+2\hat{k}$ , $\hat{i}+2\hat{j}-2\hat{k}$ and…MediumSingle correct
7 Apr 2025, Shift 2 · Q15Let $\vec{a}$ and $\vec{b}$ be the vectors of the same magnitude such that…MediumSingle correct
8 Apr 2025, Shift 2 · Q14Let $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$ and $\vec{b} = 2\hat{i} + \hat{j} - \hat{k}$ . Let $\hat{c}$ be a unit vector in the plane of…MediumSingle correct
8 Apr 2024, Shift 1 · Q18The set of all $\alpha$ , for which the vectors $\vec{a}=\alpha t\hat{i}+6\hat{j}-3\hat{k}$ and…MediumSingle correct

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.